Is there a way to put a temporary effect on a weapon that will persist for a time?
Eg poisons are one hit per application....but I'm thinking mostly of effects like fire damage etc.

At the moment I carry a few weapons with different effects like fire or frost etc to use on different enemies.
It would be great to be able to have one weapon and be able to adapt it to my enemies on the fly.

Any way to do this?

Nope. The closest you can come to what you want is to max out Enchanting in order to get the extra effect perk. That way, you could put both fire and shock on a weapon, or whatever combo you wish. But you'd still have to carry 2 weapons to cover all 3 elemental damage types.